Fraction to Decimal Converter
Enter a numerator and denominator and this converter shows the decimal value, the equivalent percentage, and the fraction reduced to lowest terms. It works with proper fractions (like 3/4), improper fractions (like 7/4), and negative values.
- Decimal
- 0.75
- Percentage
- 75%
- Simplified fraction
- 3/4
Converting fractions to decimals comes up constantly: reading measurements, understanding odds, scaling recipe quantities, interpreting statistics. The conversion is a single division, but simplification and repeating decimals trip people up, so this tool handles both.
How it's calculated
Decimal = numerator ÷ denominator
The percentage is the decimal multiplied by 100. To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). For example, GCD(18, 24) = 6, so 18/24 reduces to 3/4.
Worked example
The fraction 18/24: 18 ÷ 24 = 0.75, which is 75%. Its simplified form is 3/4. The fraction 1/3 gives 0.3333…, a repeating decimal, commonly rounded to 0.333 or shown as 33.33%.
Frequently asked questions
›What is a repeating decimal?
A decimal whose digits repeat forever, like 1/3 = 0.333… or 1/7 = 0.142857142857…. A fraction produces a repeating decimal whenever its simplified denominator has a prime factor other than 2 or 5.
›How do I convert a decimal back to a fraction?
Write the decimal over a power of ten and simplify: 0.625 = 625/1000 = 5/8. Repeating decimals need an algebraic trick; for example, 0.333… equals exactly 1/3.
›What is an improper fraction?
A fraction whose numerator is larger than its denominator, like 7/4. Its decimal is greater than 1 (7/4 = 1.75), and it can also be written as the mixed number 1¾.
›What are common fraction-to-decimal equivalents?
Worth memorizing: 1/2 = 0.5, 1/3 ≈ 0.333, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 3/4 = 0.75, and 7/8 = 0.875.
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